How to crack this one ?
Prove that the equation
\[6(6a^2 + 3b^2 + c^2) = 5n^2\]
has no solutions in integers except $a = b = c = n = 0$.
APMO 1989
- nafistiham
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\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.
Re: APMO 1989
The first thing that came to my mind after seeing $3,6$ and the squares is It should work I believe.
"Everything should be made as simple as possible, but not simpler." - Albert Einstein
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Re: APMO 1989
Solved here.nafistiham wrote: ↑Mon Apr 09, 2012 9:16 pmHow to crack this one ?
Prove that the equation
\[6(6a^2 + 3b^2 + c^2) = 5n^2\]
has no solutions in integers except $a = b = c = n = 0$.